Showing papers in "Journal of Chemical Physics in 1942"

Intramolecular Energy Transfer The Fluorescence of Complexes of Europium

Abstract: The characteristic line fluorescence of trivalent europium is excited in certain organoeuropium compounds by irradiation with light absorbed only by the organic part of the compound. The efficiency of excitation varies greatly with the nature of the compound, temperature, and solvent. Under optimum conditions, i.e., solution of a covalent compound at liquid‐air temperature, almost unit efficiency has been obtained. The decay time of the fluorescence is independent of quenching; quenching prevents excitation of the europium ion. There seems to be a steady gradation of efficiency of transfer from covalent to ionic compounds.

Energy Levels and Thermodynamic Functions for Molecules with Internal Rotation I. Rigid Frame with Attached Tops

Abstract: A general treatment of internal rotation is given for molecules whose moments of inertia for over‐all rotation are independent of internal rotational coordinates. Tables are presented for the various thermodynamic functions which are accurate for molecules with one internal rotation and for the potential energy (V/2) (1 — cos nφ). The tables are shown to be a good approximation for molecules with several internal rotational coordinates, provided the potential energy can be expressed as a sum of terms of this type. Methods are suggested for treating problems where cross terms involving more than one internal coordinate are present in the potential energy. The energy level expressions are developed for the more general case with the potential energy expressed by a Fourier series. Although a few specific cases were worked out with different shape potential barriers, it appears that the simple form assumed above will be satisfactory for many purposes.

Dispersion and Absorption in Dielectrics II. Direct Current Characteristics

Abstract: In the first paper of this series [J Chem Phys 9, 341 (1941)], it was shown that the complex dielectric constant, e*, of many liquid and solid dielectrics is given by a single very general formula e*=e∞+(e0−e∞)/[1+(iωτ0)1−α] In this equation e0 and e∞ are the ``static'' and ``infinite frequency'' dielectric constants, ω = 2π times the frequency, τ0 is a generalized relaxation time and α is a constant, 0 < α < 1 The transient current as a function of the time, t, after application of a unit constant potential difference has been calculated from this expression in series form For times much less than τ0, the time dependence is of the form (t/τ0)−α, and for times much greater than τ0, it is of the form (t/τ0)−(2—α) The transition between these extremes occurs for the range in which t is comparable with τ0 The total absorption charge, which is the integral of the exact expression, is always finite Although many transient data for dielectrics are of the predicted form, none have been taken over a suff

X‐Ray Interference in Partially Ordered Layer Lattices

Abstract: The x‐ray interference is calculated for layer lattices in which the phase shifts between consecutive layers and the scattering powers of individual layers do not follow a strictly periodic arrangement. In the second section the scattering power of all layers is assumed to be the same but the phase shifts can take on different values. In the third section neither the scattering powers nor the phase shifts have fixed values but a simplifying assumption is made about the phase shifts according to which distances between neighboring layers can be represented as sums of two distances characteristic of the individual layers. In both these sections a random sequence of the layers is assumed. In the fourth section the problem of arbitrary scattering powers and phase shifts is treated, and furthermore a statistical correlation between neighboring layers is introduced. In the following section the general theory is applied to a specific partially ordered stacking of layers encountered in micas and other similar minerals. The last section treats irregularities in close packed structures of spheres and irregular sequences of layers in graphite.

The Radial Distribution Function in Liquids

Abstract: In accordance with the general methods of an earlier paper (reference 1) an integral equation is evolved for the radial distribution function for pairs in a liquid, and an approximate solution is effected for a system of ``hard spheres.'' The form of the function depends on a single parameter λ which can be related to certain observed physical properties of the liquid and to the diameter of closest approach. The theoretical function has been calculated for a value of λ appropriate to liquid argon at 90°K, and compared to experimental radial distribution functions derived from x‐ray scattering data.

Polarization of Light Scattered by Isotropic Opalescent Media

Abstract: A general study is given of the polarization of light scattered by isotropic media whose elements of heterogeneity are not very small in comparison with the wavelength, (suspensions, colloidal solutions, solutions of large molecules, ...). This includes an extension of a theory by R. S. Krishnan, who, considering certain particular states of polarization of the incident light and applying the law of reciprocity, had proved the equality of two of the four coefficients which are to be considered in these cases. Using Stokes' linear representation of the polarization of light beams, it is shown that the scattering through a given angle and for a given wave‐length is characterized by the 16 coefficients of the linear forms which express the four polarization parameters of the scattered beam in terms of the four corresponding parameters of the incident beam and that the law of reciprocity leads to six relations between these sixteen coefficients. For an isotropic asymmetrical medium (having rotatory power), th...

Statistical Thermodynamics of Rubber. III

Abstract: The entropy change for the stretching of rubber is calculated by statistical methods, neglecting intermolecular attractions and deformation of bonds and bond angles. The calculation involves the probability of finding the system with a given distribution of molecular configurations. An equation of state relating the tension, length, and temperature of a rubber band is then derived. Following this a discussion of the applicability and the limitations of the theory is presented.

The Vibrational Spectra of Pyrrole and Some of Its Deuterium Derivatives

Abstract: The Raman spectra of pyrrole, pyrrole‐N‐d, symmetrical pyrrole‐d4, and pyrrole‐d5 have been studied with a high speed grating spectrograph. The infra‐red absorption spectra of the same compounds have been investigated in the liquid state in the region 750–1900 cm−1. With the help of the selection principles and Teller's product rule, these spectra have been analyzed for a molecule of C2v symmetry. The analysis yields values for all but one of the twenty‐four fundamental frequencies, and this one has been estimated. The spectra indicate clearly a C2v structure for pyrrole, although a Cs (non‐planar) structure cannot yet be rigorously excluded.

Frequency Spectrum of Crystalline Solids

Abstract: It is generally accepted that a normal crystalline solid can be pictured at absolute zero as an assembly of molecules arranged at periodically placed lattice points. Since at higher temperatures each molecule becomes a harmonic oscillator about its lattice point, in order to calculate thermodynamic properties of the crystal it is necessary to know the distribution of its internal normal modes of vibration. On the basis of the Born‐von Karman model these normal modes of vibration are roots of a secular determinant. In this paper it is shown that the 2nth moment of the distribution function of normal modes is proportional to the trace of the nth power of the matrix of the Born‐von Karman determinant. By expressing the distribution function as a linear combination of Legendre polynomials it is shown that the coefficient of each polynomial is a linear combination of the moments. The frequency distribution function of a two‐dimensional simple cubic lattice is calculated by the above method and turns out to have two maxima. Usually the equation for a thermodynamic function F(T) involves the integral of the product of the frequency distribution function g(v) and a known function K(T, v). We show here that when F(T) is a known function of T an integral equation results with g(v) under the integral sign. This integral equation can be solved for g(v) by use of Fourier transforms.

Second Virial Coefficients and the Forces Between Complex Molecules

Abstract: The second virial coefficients of ethane, propane, n‐butane, n‐heptane, ammonia, methyl chloride, and the freons are computed from available experimental data. The causes for sizeable errors in second virial coefficients are considered. At temperatures above the critical, the second virial agrees with the theorem of corresponding states. Below the critical temperature, molecules with dipoles have unusually large virials and the values of their reduced dipole moment, μ/(TcVc)½, determine the discrepancy. The data for isomeric hydrocarbons show that the second virial is not sensitive to the shape of the molecule. This makes it impossible to determine the exact laws of intermolecular interaction from the temperature variation of the second virial. The imperfections of a gas are considered to arise from the presence of double molecules which exist for the duration of a collision. The equilibrium constant for the formation of double molecules is related to the second virial and its temperature variation gives ...

The Infra‐Red Absorption Spectra of Ethylene and Tetra‐Deutero‐Ethylene under High Resolution

Abstract: The fine structure of several infra‐red absorption bands of C2H4 and C2D4 have been resolved. From the rotational constants so found, the C–C and C–H distances in this molecule were calculated to be 1.353 and 1.071A, and the H–C–H angle to be 119°55′. An assignment of fundamental frequencies has been made which is consistent with the observed data.

Contribution to Statistical Mechanics

Abstract: The method of the grand partition function may be used to calculate distribution functions Fn(z, {n}) proportional to the probability that n molecules in a system of fugacity z, and fixed temperature, occupy the position of their coordinates symbolized by {n}. The method makes use of the distribution functions Fn(0, {n}) at zero fugacity. The distribution functions may be written Fn(z, {n})=exp[−Wn(z, {n})/kT], in which Wn(z, {n}) is the potential of average force of n molecules at the fugacity z, which becomes equal to the ordinary potential energy at zero fugacity. The equations may be generalized to permit the calculation of the distribution functions at any fugacity assuming a knowledge of them at any other fugacity. Using methods previously employed for imperfect gases, the pressure, and also the density in molecules per unit volume, may be developed in a power series of difference of fugacity around any arbitrary fugacity. The coefficients of these developments are calculable at all fugacities by th...

The Approximate Solution of Schrödinger Equations by a Least Squares Method

Abstract: A method of approximation to the solution of a Schrodinger equation has been developed in which variation functions are used but no integrations are involved. The procedure involves the evaluation of the energy for a set of representative points in configuration space. The parameters in the variation function are then chosen by applying the condition that the mean square deviation of the energy from the average should be a minimum.

Energy Relations of the Surface of Solids I. Surface Energy of the Diamond

Abstract: From the known structure of the diamond the total surface energy of the crystal has been calculated in terms of the energy of the carbon‐carbon bond, and is found to be: 1.50×10−9EB erg cm−2 for the 111 face, and 2.10×10−9EB erg cm−2 for the 100 face, where EB is the energy in ergs per bond. If the bond energy is assumed to be 90 kcal. mole−1 the values become 5650 erg cm−2 for the 111 face, and 9820 erg cm−2 for the 100 face. The corresponding free surface energies are found to be: 111 face at 25°=5400 erg cm−2 100 face at 25°=9400 erg cm−2. One uncertain feature in the calculation is that involved in the calculation of the decrease in energy caused by the long range binding of the valence bonds in the surfaces. In the 111 face the bonds are 2.517A apart, and are perpendicular to the surface. Thus the bond directions are parallel, while inside the diamond the carbon‐carbon distance is only 1.54A, and the bonds meet head on. While in the 111 face there is only one bond per carbon atom, in the 100 face the...

Absorption of Polysubstituted Benzene Derivatives

Abstract: The intensification, by nonchromophoric substitutions, of the forbidden, 1A1g→1B2U, transition in benzene is due, on the one hand, to the unsymmetrical distortion of the ring by the normal vibrations and, on the other hand, to the transition moment produced at the equilibrium position by the migration of charge from the substitution into the ring or vice versa. The latter effect is treated by the method of antisymmetrical molecular orbitals, all calculations being limited to the first order. The rules for combining transition moments due to the various groups in a polysubstituted benzene are calculated. It is shown that, for weak nonchromophoric substitutions, the intensity ratios (except for the less important variation in the normal vibrations) are for C6H5X:oC6H4X2:mC6H4X2:pC6H4X2:1,3,5 C6H3X3:1,2,3 C6H3X3:1,2,4 C6H3X3=1:1:1:4:0:0:3. It is further shown that if one substitutes benzene by a meta‐directing group, M, and by an orthopara‐directing group, P, of the same intensifying power, the ratios for th...

Mechanism of the Thermal Reaction Between Hydrogen and Oxygen

Abstract: Explosion limits and reaction rates of hydrogen and oxygen have been measured in spherical quartz and Pyrex vessels of varying diameter, clean and coated with various substances and for various temperatures, pressures, and mixture compositions, including addition of inert gases. Clean and B2O3‐coated surfaces give rise to rapid and erratic reaction, indicating a surface chain‐breaking efficiency e≪λ/d (ratio of mean free path to vessel diameter); the reaction is self‐accelerating, probably due to poisoning of the surface by H2O, which decreases e. By coating with various salts such as KCl, BaCl2, K2B2O4, K2B4O7, and Na2WO4, the condition e≫λ/d is established in the region between second and third explosion limits. The limits are farther apart, the rates much lower and not accelerating, and both rates and limits are reproducible and identical for the various salts. For K2B4O7, e≃λ/d for small reaction rates. The chain‐breaking mechanism on clean and salt‐coated surfaces is discussed. With the elimination o...

The Conductance and Ionic Mobilities for Aqueous Solutions of Potassium and Sodium Chloride at Temperatures from 15° to 45°C

Abstract: The conductance of aqueous solutions of potassium and sodium chloride has been determined at 15, 25, 35 and 45°C for concentrations from 0.0005N to 0.01N by a modified direct‐current method of high precision. At 15° and 25°, the results are in highly satisfactory agreement with the best of the existing data obtained by the a.c. bridge method. For all temperatures, the conductance can be represented within a few hundredths of a percent by the extended Onsager‐Shedlovsky equation. A calculation of the mobility of chloride ion from the conductance and the transference numbers obtained in this laboratory shows that for all temperatures the Kohlrausch rule of independent ionic mobilities is obeyed at infinite dilution within the apparent limit of error of the measurements—0.02 to 0.03 percent. The conductance and ionic mobilities for round values of the concentration, and the temperature coefficients of the ionic mobilities at infinite dilution are tabulated.

The Mechanism of Processes Initiated by Excited Atoms I. The Quenching of Excited Sodium

Abstract: The potential‐energy surfaces relevant to a number of simple processes involving excited (2P) sodium have been constructed, and the mechanism of the reactions discussed in terms of them and of the theory of absolute reaction rates. It is shown that quenching by atoms is normally a very inefficient process, the effect of additional atoms in a quencher being to stabilize a quenched complex, commonly a polar compound, which finally decomposes to give the deactivated atom and a vibrationally excited product. The activated state may be either at the top of a rotational‐energy barrier or at a crossing point to a polar surface, and the theory is shown to be consistent with the experimental values of the quenching cross sections. In the cases examined the quenching is of a physical nature, the energy passing chiefly into vibrational energy, with a certain amount going into translational and rotational degrees of freedom. Saturated hydrocarbons appear to quench like hydrogen except that there is probably a small e...

A Superliquid in Two Dimensions and a First‐Order Change in a Condensed Monolayer II. Abnormal Viscosity Relations of Alcohol Monolayers in Condensed Liquid Phases

Abstract: The new LS phase found in alcohol monolayers has the compressibility of a solid and, at temperatures near that of the first‐order L2⇌LS transition, the low viscosity of a very highly fluid liquid. The viscosity is almost independent of pressure, but varies in an abnormal way with temperature. For example, octadecanol exhibits a minimum viscosity at about 8.8°C. As is normal, the viscosity increases with decrease of temperature over the small range from 8.8° to 7.5°C where a transition to the S phase occurs. However, above 8.8°C an increase of temperature of 16° increases the viscosity of the LS phase by a factor of 25, and changes it from Newtonian to non‐Newtonian. At a pressure of 18 dynes cm−1 the logarithm of the viscosity above 12°C varies nearly either as T, or as 1/T. At other pressures (Fig. 5) the relations are different. At 1 dyne cm−1 the viscosity of the condensed liquid (L2) phase decreases in a normal way with temperature, but at 12 dynes cm−1 the relation is reversed and is abnormal, since the viscosity increases very rapidly as the temperature rises, to correspond with that of the LS phase. This makes the pressure relations extremely abnormal, since the LS phase at 25°C and the S phase at 5°C do not differ greatly in their behavior from normal liquids, which follow the relation log η=log η0+kπ. However, at the intermediate temperatures in the range of 8.85 to 10° the viscosity of this phase decreases only slowly with pressure at low pressure, but more and more rapidly as the pressure increases, until the extremely rapid decrease is stopped by a transition to the LS phase. The viscosity relations indicate that the transition S⇌LS occurs very close to a molecular area of 19.98A2. While the area for the transition is almost constant, its temperature increases slowly with pressure. At 16 dynes cm−1 an increase of 0.07A in mean molecular distance increased the viscosity by a factor of 55. It should be noted that this effect is in the abnormal direction. The S phase is the only one of the three condensed phases which exhibits normal viscosity relations. In both the S and the LS phases the molecules may be assumed to be oriented perpendicular to the surface. In three‐dimensional crystals the hydrocarbon chains occupy an area of 18.5A2, in the S alcohol films from 19.5 to 20.0A2, in the LS films from 20 to 20.75, and in the L2 films from 19.8 to 22.7. The highest temperature employed was 35°C. An increase above this temperature would increase the upper limits of area for the LS and L2 monolayers. It is obvious that the possibility exists for hydrogen bonding between the —OH groups of the alcohols themselves, or between these groups and the water molecules. What is needed for the explanation of the abnormal relations of the L2 and LS phases of the alcohols is to determine what type of binding will increase in energy as the molecular distance is increased, either by increase of temperature or decrease of pressure. The normal behavior of the solid surface phase of the alcohols is similar to that of the acids, which has been discussed in earlier papers.

Infra‐Red and Raman Spectra of Polyatomic Molecules XVII. Methyl‐d3‐Alcohol‐d and Methyl‐d3‐Alcohol

Abstract: CD3OD and CD3OH have been prepared and their infra‐red spectrum in the range from 2.5μ to 18μ has been measured. The Raman spectrum of CD3OD has been observed. CH3OH and CH3OD have been reinvestigated and an assignment for all four methyl alcohols has been given.

Solid Solutions of the Alkali Halides

Abstract: X‐ray studies of solid solutions of alkali halide pairs with a common ion at room temperature and at 550°C show that these pairs can be divided into three groups depending on the percent deviation δ of their lattice parameters For values of δ less than 6 percent miscibility is complete at room temperature For values of δ between 6 and 13 percent miscibility is complete at 550°C For values of δ larger than about 13 percent miscibility is not complete at 550°C In terms of the Born theory of ionic lattices, the free energy of mixing, and Vegard's law, an approximate theory for the phase curve of these solid solutions is derived For a typical alkali halide with an electrostatic energy of 180 kcal at the absolute zero of temperature the equation of the phase curve is 9δ2/T(1–2x)+ln x−ln (1−x)=0, where x is the mole fraction of one component dissolved in the other The temperature above which miscibility is complete is given by T=45δ2 The heat of mixing is approximately −9δ2 cal The predictions of this

Infra‐Red Spectra of Hydrocarbons I. Some Investigations of the Temperature Dependence of Absorption Bands

Abstract: Theory indicates that the separation of the maxima of the P and R branches of an infra‐red band should be proportional to the square root of the absolute temperature. This relation has been tested by experiments with ethane, propylene and 2, 2‐dimethyl butane in which the temperature was varied between − 195°C and room temperature. It has been found that the relation is approximately valid, the band widths being somewhat less than theory predicts in the liquid and considerably less in the solid. The positions of the bands are independent of the temperature in 2, 2‐dimethyl butane and only slightly affected in the other compounds. Some bands of propylene display a pronounced variation in relative intensity with temperature. The usefulness of spectra obtained at low temperatures in the theoretical assignment of fundamentals, as a tool for the study of the liquid state and for analytical purposes, is pointed out.

The Derivation of a General Kinetic Equation for Reaction Between Ions and Dipolar Molecules

Abstract: An equation has been derived for the reaction rate constant in the case of ion‐dipole reactions. Section II contains the extension of Debye‐Huckel's theory of ionic atmospheres to the case of dipoles surrounded by ions, coupling it with Onsager's theory of electric moments of molecules in liquids. Section III applies the potential constructed to the derivation of the rate constant by the kinetic procedure of Christiansen and Scatchard. The result is substantiated by existing data both from concentration and dielectric constant dependence of the rate of reaction between ions and dipoles (Section IV).

The Crystal Structure of Hydrazinium Difluoride

Abstract: An x‐ray analysis shows that crystalline hydrazinium difluoride is built upon a rhombohedral unit cell having a0=5.43A, α=38°10′, containing one molecular formula. The positions of the atoms have been determined and correspond to trans‐hydrazinium ions which form linear hydrogen bonds to fluoride ions at the corners of an elongated octahedron. Each fluoride ion forms three hydrogen bonds to different hydrazinium ions, and condenses the octahedra into continuous layers. As a result of the packing of these layers to build up the structure, each nitrogen atom comes in contact with an ``extra'' fluoride ion and thereby assumes a coordination number of 5. Analysis of the N–N and N–H≡F distances of 1.42A and 2.62A, respectively, shows that each atom in the hydrazinium ion bears approximately ¼ of a unit of positive charge. The bearing of the structure of the ion on the adjacent charge rule is discussed. Some of the properties of the ion are interpreted in terms of the structure.

Statistical Mechanics of Nearest Neighbor Systems II. General Theory and Application to Two‐Dimensional Ferromagnets

Abstract: This is a continuation of an effort to reduce to the solution of a characteristic value problem the rigorous calculation of thermodynamic properties of systems in which the intermolecular forces are sufficiently short ranged so that practically the entire potential energy of the system results from interactions between nearest neighbors. The partition function of such a system can be expressed in terms of the largest characteristic value of a linear operator equation and finally as the ratio of partition functions of systems with relatively few particles whose potential energy functions differ somewhat from those in the original system. A method of evaluating grand partition functions and one of introducing interactions between more distant neighbors are discussed. The general theory is applied to the calculation of magnetization, internal energy, and specific heat of two‐dimensional ferromagnets on the basis of the Ising model. There seems to exist a λ‐point phase transition in the change from ferromagnetic to nonferromagnetic states.

Raman Spectra of Compounds in the Gaseous and Liquid States

Abstract: An apparatus for exciting the Raman spectra of gases and liquids at temperatures up to 300°C is described. For phosphorus trichloride, methyl chloride, methyl bromide, methyl alcohol, methylene chloride, methylene bromide, chloroform, and carbon tetrachloride, the Raman spectra of the gas and the liquid at the same temperature have been photographed in juxtaposition with a liquid‐prism spectrograph of speed f: 2.9 and linear dispersion 27A/mm at 4400A. The Raman spectra of gaseous n‐pentane, n‐hexane, and deuterium oxide have been photographed with 2537A excitation. The change in the Raman frequencies with the state of aggregation is different for different vibrations and varies greatly from compound to compound. In the absence of an adequate theory for this phenomenon, a search has been made for empirical regularities. The perpendicular bands of the symmetrical‐top molecules are much less diffuse in the liquid than in the gas, showing that the intermolecular forces are effective in quenching the rotation of the molecules in the liquid. The other bands are about equally sharp in gas and liquid.

Energy Relations of the Surfaces of Solids II. Spreading Pressure as Related to the Work of Adhesion Between a Solid and a Liquid

Abstract: This is the second paper in a series which gives theoretical values for the free and total surface energy of the diamond, and experimental values for the total and free energy, the latent heat, and the entropy of adhesion between various crystalline solids and liquids. This second paper deals with the oldest part of the subject, but a part which has always been treated incorrectly. The total energy (eA(SL)) required to separate water from solids of the general type of BaSO4, TiO2, and ZrSiO4, has been found by Harkins and Boyd to vary from 600 to 1000 erg cm−1, while to separate octane from these solids requires only from 150 to 250 erg cm−2. The free energy of separation, designated by WA(SL), is smaller. It is generally believed that WA(SL)=γL(1+cos θSL), which gives values, for solids thus far investigated, from 47.5 to 144 erg cm−2 at 25°C if the liquid is water, and much smaller values if organic liquids are used. Indeed the maximum value of the work of adhesion between water and any solid at this te...